# Entanglement production in the dynamical Casimir effect at parametric resonance

## TL;DR

This paper analytically studies entanglement growth in the dynamical Casimir effect at parametric resonance, revealing dimension-dependent entropy scaling and unique properties of bosonic field theories.

## Contribution

It provides the first analytical computation of entanglement entropy evolution in the dynamical Casimir effect at resonance across arbitrary dimensions.

## Key findings

- In (1+1)D, entanglement entropy grows logarithmically over time.
- In higher dimensions, entropy growth is linear with time.
- The logarithmic growth has a unique 1/2 pre-factor specific to bosonic fields.

## Abstract

The particles produced from the vacuum in the dynamical Casimir effect are highly entangled. In order to quantify the correlations generated by the process of vacuum decay induced by moving mirrors, we study the entanglement evolution in the dynamical Casimir effect by computing the time-dependent R\'enyi and von Neumann entanglement entropy analytically in arbitrary dimensions. We consider the system at parametric resonance, where the effect is enhanced. We find that, in (1+1) dimensions, the entropies grow logarithmically for large times, $S_A(\tau)\sim\frac{1}{2}\log(\tau)$, while in higher dimensions (n+1) the growth is linear, $S_A(t)\sim \lambda\,\tau$ where $\lambda$ can be identified with the Lyapunov exponent of a classical instability in the system. In $(1+1)$ dimensions, strong interactions among field modes prevent the parametric resonance from manifesting as a Lyapunov instability, leading to a sublinear entropy growth associated with a constant rate of particle production in the resonant mode. Interestingly, the logarithmic growth comes with a pre-factor with $1/2$ which cannot occur in time-periodic systems with finitely many degrees of freedom and is thus a special property of bosonic field theories.